In medical imaging, as well as other imaging technologies, signal-to-noise ratio (“SNR”) is utilized as a quantitative measure of image quality. Generally, SNR is defined as the ratio between the mean intensity value and the root-mean-square (“RMS”) noise, σ, in an image. The term “net signal” refers to the difference between an average signal value over the image, and background values, whereas the term RMS noise refers to the standard deviation of the noise value in the image. As SNR decreases in a medical image, it becomes increasingly more difficult to differentiate between anatomical features and other clinical findings of importance to the clinician. Thus, it is generally desirable to provide a relatively high SNR in medical imaging applications.
Spatial resolution is typically balanced with respect to the achievable SNR in an image. For example, the traditional relationship between spatial resolution, Δx, in a two-dimensional image and the achievable SNR in that image is given by:
                              σ          2                ∝                              1                          Δ              ⁢                                                          ⁢                              x                3                                              .                                    (        1        )            
Thus, as spatial resolution becomes finer, the noise variance, σ2, present in the image increases significantly. The SNR characteristics of an image are also governed by the manner in which image data is initially acquired. In many instances, it may be beneficial to alter data acquisition parameters, such as decreasing radiation dose or scan time, to the betterment of the subject of the examination, but to the detriment of SNR in the resultant images.
When parameters of an x-ray imaging study, such as tube current and tube current time product, “mAs,” are varied in order to decrease the radiation dose imparted to the subject, the SNR of the resultant images suffers. For example, decreasing tube current produces a related decrease in radiation dose; however, the noise present in the resultant images is increased, thereby affecting SNR in accordance with the following relationship:
                              SNR          =                                    μ              σ                        ∝                          Dose                        ∝                          mAs                                      ;                            Eqn        .                                  ⁢                  (          2          )                    
where μ is the measured linear attenuation coefficient and σ is the RMS noise. Thus, if mAs is reduced by half, SNR will decrease by a factor of √{square root over (½)}, which corresponds to about a thirty percent decrease in SNR. Thus, while decreasing mAs during an x-ray imaging study provides a beneficial decrease in radiation dose imparted to the subject being imaged, the resultant images suffer from increased noise and, therefore, decreased SNR. Such images have limited clinical value.
Depending on the technique used, many magnetic resonance imaging (“MRI”) scans currently require many minutes to acquire the necessary data used to produce medical images. The reduction of this scan time is an important consideration, since reduced scan time increases patient throughout, improves patient comfort, and improves image quality by reducing motion artifacts. Many different strategies have been developed to shorten the scan time, including so-called parallel MRI (“pMRI”) techniques.
While the use of parallel MRI acts to decrease the amount of time required to image a subject without increasing gradient switching rates or RF power, parallel MRI methods are plagued with losses in signal-to-noise ratio (“SNR”). In general, the SNR of an image reconstructed using parallel MRI methods is decreased in accordance with the following relationship:
                              SNR          ∝                      1                          g              ⁢                              R                                                    ;                            Eqn        .                                  ⁢                  (          3          )                    
where g is the so-called geometry factor, or “g-factor,” and R is the acceleration factor, which describes the degree of undersampling employed and is related to, and generally limited by, the number of receiver coils in the array. Thus, parallel MRI methods suffer from a reduction in achievable SNR, offsetting the benefits provided by decreased scan time requirements.
It would therefore desirable to provide a method for image reconstruction or image processing in which an image having high SNR and high spatial resolution can be produced.